[Executive summary: Emacs is mostly reproducible. For those who want to know what reproducibility is and why they should care, see: https://reproducible-builds.org/
There has recently been a lot of discussion about reproducible builds on gnu-prog-discuss, and bugs have been filed against Emacs.
As well as working on GNU Emacs, I'm a Debian Maintainer who recently sat through a progress update at the November MiniDebConf in Cambridge, England, on the subject of reproducible builds, so I thought it would be worth seeing how GNU Emacs is doing currently.
Since I'm familiar with Debian, and since much of the work on reproducible builds was started there and is most advanced there, I checked the current Debian source package for Emacs 25.1.
I found that it has no patches for reproducibility. This is a good thing! (Debian has already patched many of its packages to make them reproducible, and over three quarters of its software packages are currently reproducible, including most GNU packages.)
I then checked the status for the reproducibility of the package, at:
This mentions two problems. The first, about build paths, is not Emacs-specific. The second, about timestamps in autoloads, is already fixed in Git (the fix will be in Emacs 26).
Conclusion: Emacs is mostly reproducible. (The requirement to be reproducible with different build paths is a recent addition to the list at reproducible-builds.org
.) The configuration option --disable-build-details can be used to omit some information, such as build host name, which make the build not reproducible across machines.
(Guidelines for the GNU Coding Standards are currently in preparation.)